Fernandez Israel, Frenking Gernot
Fachbereich Chemie, Philipps-Universität Marburg, Hans-Meerwein Strasse, 35043 Marburg, Germany.
J Phys Chem A. 2007 Aug 16;111(32):8028-35. doi: 10.1021/jp073737k. Epub 2007 Jul 14.
DFT calculations at the BP86/TZ2P level have been carried out for the primary, secondary, and tertiary carbenium ions H2C-CH(EH3)2 (1a-e), HC{CH(EH3)2}2, (2a-e), and C{CH(EH3)2}3 (3a-e) for E = C, Si, Ge, Sn, Pb. The nature of the interaction between the carbenium center H(2-n)C(+) and the substituents {CH(EH3)2}m has been investigated with an energy decomposition analysis (EDA) aiming at estimating the strength of the pi hyperconjugation which electronically stabilizes the carbenium ions. The results of the EDA show that the calculated DeltaEpi values can be used as a measure for the strength of hyperconjugation in carbenium ions arising from the interactions of saturated groups possessing pi orbitals. The theoretical data suggest that the ability of sigma C-E bonds to stabilize positive charges by hyperconjugation follow the order C < Si < Ge < Sn < Pb. Hyperconjugation of C-Si bonds is much stronger than hyperconjugation of C-C bonds while the further rising from silicon to lead is smaller and has about the same step size for each element. The strength of the hyperconjugation in primary, secondary, and tertiary alkyl carbenium ions does not increase linearly with the number of hyperconjugating groups; the incremental stabilization becomes smaller from primary to secondary to tertiary cations. The effect of hyperconjugation is reflected in the shortening of the C-C bond distances and in the lengthening of the C-E bonds, which exhibits a highly linear relationship between the calculated C-C and C-E distances in carbocations 1-3 and the hyperconjugation estimated by the DeltaEpi values.
已在BP86/TZ2P水平上对E为C、Si、Ge、Sn、Pb的伯、仲和叔碳正离子H2C-CH(EH3)2 (1a - e)、HC{CH(EH3)2}2 (2a - e)和C{CH(EH3)2}3 (3a - e)进行了密度泛函理论（DFT）计算。利用能量分解分析（EDA）研究了碳正离子中心H(2 - n)C(+)与取代基{CH(EH3)2}m之间的相互作用性质，旨在估算使碳正离子电子稳定的π超共轭强度。EDA结果表明，计算得到的ΔEpi值可作为衡量由具有π轨道的饱和基团相互作用产生的碳正离子中超共轭强度的指标。理论数据表明，σ C - E键通过超共轭稳定正电荷的能力顺序为C < Si < Ge < Sn < Pb。C - Si键的超共轭比C - C键的超共轭强得多，而从硅到铅的进一步增强较小，且每个元素的步长大致相同。伯、仲和叔烷基碳正离子中超共轭的强度并不随超共轭基团数量线性增加；从伯碳正离子到仲碳正离子再到叔碳正离子，增量稳定作用变小。超共轭效应体现在C - C键距离的缩短和C - E键的延长上，在碳正离子1 - 3中计算得到的C - C和C - E距离与由ΔEpi值估算的超共轭之间呈现出高度线性关系。
